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Design >> Mixed-Signal Design >> Z domain model for this sigma-delta modulator
https://designers-guide.org/forum/YaBB.pl?num=1232542360

Message started by neoflash on Jan 21^st, 2009, 4:52am

Title: Z domain model for this sigma-delta modulator
Post by neoflash on Jan 21^st, 2009, 4:52am

This model is different from traditional modulator.

Could any one help derive the Z-domain model for this modulator?

I have one in mind but that looks involves a (1-Y) scaler at input. Thus make it looks strange. Hope some people familiar with this could help.

Title: Re: Z domain model for this sigma-delta modulator
Post by Berti on Jan 21^st, 2009, 10:15pm

Hi neonflash,

To me it looks that this model consist of discrete-time, continuous-time and non-linear blocks. Besides choosing a linearized model for the quantizer one needs to know how the switches work in order to apply the correct transformation.

Regards

Title: Re: Z domain model for this sigma-delta modulator
Post by neoflash on Jan 22^nd, 2009, 5:05am

We could treate Integrator as Z^-1/(1-Z^-1)

Title: Re: Z domain model for this sigma-delta modulator
Post by ywguo on Jan 23^rd, 2009, 5:45pm

neoflash,

I guess a and b all independent inputs. Y is the output. As the quantized output Y is not fed back to the input, the quantization noise is not modulated actually. What I have derived is shown below.

Y(Z)=a(Z)(z^-1/(1-z^-1)) + E(Z); if Y(Z-1)<0
Y(Z)=b(Z)(z^-1/(1-z^-1)) + E(Z); if Y(Z-1)>0

Yawei

Title: Re: Z domain model for this sigma-delta modulator
Post by neoflash on Jan 24^th, 2009, 1:33am

Then, how we compute the TF for Y, from a and b?